After a brief review of the history and philosophy of neural modelling, several attractor neural networks are studied in some detail. Firstly a variation of the Hopfield Model employed to perform symmetry invariant pattern recognition is considered. It is shown that parallel dynamics tend to perform a symmetry-transformationof the network configuration at each update. In contrast serial dynamics tend to drive the network configuration into a symmetry invariant. The component of the interactions that drive the aforementioned dynamic tendencies act as a noise upon the Hopfield interactions. However replica symmetric theory shows that an extensive number of patterns may be stored whilst allowing symmetry invariant pattern recognition. The performance of Gardner optimal interactions, that optimise the performance of a perceptron, is examined in the context of attractor neural networks. The discussion is restricted to randomly dilute networks for which dynamical equations for the overlaps are available. A general analysis of these equations is performed and the transitions to no memory categorised. In particular the conditions for a point, tricritical in nature, to exist in the α<i>T</i>- plane are derived. Retrieval phase diagrams for the optimal interactions with and without errors in storage are constructed. The case of sparse spatial coding is then investigated by considering two connection rules, Covariance and Willshaw, that have the storage capacities of the form of the Gardner optimal connections as the bias of the patterns becomes very large. In both cases the choice of threshold is crucial in order to achieve maximum storage, and also controls the basins of attraction of the memories. Both connection schemes exhibit an undesirable high activity attractor, but in the Willshaw case this may be suppressed by introducing an activity dependent inhibition. In order to bring network models into close contact with biological experiment, the problem of firing rates is discussed. A model is then proposed that uses a biologically realistic dynamics and incorporates a variety of other biological features. Graphic displays from computer simulation of the model are presented and associative retrieval can be seen to occur whilst the network functions in a manner that is reminiscent of the results of biological experiments.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:650062 |
| Date | January 1990 |
| Creators | Evans, Martin |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/14810 |
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